Generalized Virial Identities: Radial Constraints for Solitons, Instantons, and Bounces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910117977391104 |
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| author | Lozano-Mayo, Jonathan |
| author_facet | Lozano-Mayo, Jonathan |
| contents | We derive a continuous family of virial identities for O($n$) symmetric configurations, parameterized by an exponent $α$ that controls the radial weighting. The family provides a systematic decomposition of the global constraint into radially-resolved components, with special $α$ values isolating specific mechanisms. For BPS configurations, where the Bogomolny equations imply pointwise equality between kinetic and potential densities, the virial identity is satisfied for all valid $α$. We verify the formalism analytically for the Fubini-Lipatov instanton, BPS monopole, and BPST instanton. Numerical tests on the Coleman bounce and Nielsen-Olesen vortex illustrate how the $α$-dependence of errors distinguishes core from tail inaccuracies: the vortex shows errors growing at negative $α$ (core), while the bounce shows errors growing at positive $α$ (tail). Applications to the electroweak sphaleron, where the Higgs mass explicitly breaks scale invariance, and the hedgehog Skyrmion illustrate the formalism in systems with multiple competing length scales. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_23548 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Virial Identities: Radial Constraints for Solitons, Instantons, and Bounces Lozano-Mayo, Jonathan High Energy Physics - Theory Pattern Formation and Solitons We derive a continuous family of virial identities for O($n$) symmetric configurations, parameterized by an exponent $α$ that controls the radial weighting. The family provides a systematic decomposition of the global constraint into radially-resolved components, with special $α$ values isolating specific mechanisms. For BPS configurations, where the Bogomolny equations imply pointwise equality between kinetic and potential densities, the virial identity is satisfied for all valid $α$. We verify the formalism analytically for the Fubini-Lipatov instanton, BPS monopole, and BPST instanton. Numerical tests on the Coleman bounce and Nielsen-Olesen vortex illustrate how the $α$-dependence of errors distinguishes core from tail inaccuracies: the vortex shows errors growing at negative $α$ (core), while the bounce shows errors growing at positive $α$ (tail). Applications to the electroweak sphaleron, where the Higgs mass explicitly breaks scale invariance, and the hedgehog Skyrmion illustrate the formalism in systems with multiple competing length scales. |
| title | Generalized Virial Identities: Radial Constraints for Solitons, Instantons, and Bounces |
| topic | High Energy Physics - Theory Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2512.23548 |